We have used kinetic modelling to analyze sets of time-resolved spectroscopic data measured for hemoglobin over a range of fractional ligand photodissociation. The model used is a kinetic formulation of the two-state allosteric model extended in a minimal fashion to incorporate the geminate ligand rebinding and tertiary conformational changes detected in the measurements. The model incorporates three spectroscopically distinguishable states of unliganded hemoglobin subunits, and the kinetic description includes a stretched-exponential form for the tertiary conformational relaxation as well as a linear free energy relation connecting the quaternary transition rates for tetramers with different numbers of bound ligands. Fits using this model produce spectra for the three unliganded species which resemble the spectrum of deoxyhemoglobin and differ in a manner that is consistent with the ligand binding affinities of the species. The fits predict that both tertiary and quaternary conformational relaxations have a marked effect on the geminate ligand rebinding rate. We have also shown that a four-state allosteric model provides a common mechanistic description of the kinetics of neurotransmitter binding, channel opening and desensitization of various synaptic ionotropic receptors.